Non-linear Dependence in Stock Returns: Does Trading Frequency Matter?

The UK has a quote-driven pure dealer market structure that is very different from order driven markets such as the NYSE and Japanese markets. This paper investigates non-linear dependence in stock returns for an exhaustive sample of UK stocks for a 21 year period. The results are analysed on the basis of trading frequency. It is found that non-linear dependence is highly significant in all cases for both individual stocks and stock portfolios formed on the basis of trading frequency. The non-linear dependence is primarily over a one day interval, although statistically significant non-linear dependence exists consistently even up to five trading days. Most of the non-linear dependence is in the form of ARCH-type conditional heteroskedasticity. However, statistically significant non-linearity in addition to an EGARCH(1,1) dependence also appears to be present. This additional non-linearity is greater for individual stocks than for portfolios and greater for smaller, less-liquid portfolios. Non-linear dependence does not appear to be caused by non-stationarity in underlying economic fundamentals or by non-linearity in the conditional mean. However, low dimensional chaos is not generally supported. The limited evidence on chaotic behaviour is stronger for portfolios with long price adjustment delays across component stocks. The main results are consistent with US studies on stock indices, suggesting that the process generating non-linear dependence is not dependent on market microstructure characteristics.